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In ΔABC, ∠B = 90° and BD ⊥ AC.

(i) If CD = 10 cm and BD = 8 cm; find AD.

(ii) IF AC = 18 cm and AD = 6cm; find BD.

(iii) If AC = 9 cm and AB = 7cm; find AD.

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(i) In Δ CDB,

∠1 + ∠2 + ∠3 = 180o

∠1 + ∠3 = 90o ..... (1)(Since, ∠2 = 90o)

∠3 + ∠4 = 90o .....(2) (Since, ∠ABC = 90o)

From (1) and (2),

∠1 + ∠3 = ∠3 + ∠4

∠1 = ∠4

Also, ∠2 = ∠5 = 90o

∴ ΔCDB ~ ΔBDA (By AA similarity)

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